$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 2x + 5$ and $ BC = 6x - 7$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {2x + 5} = {6x - 7}$ Solve for $x$ $ -4x = -12$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 2({3}) + 5$ $ BC = 6({3}) - 7$ $ AB = 6 + 5$ $ BC = 18 - 7$ $ AB = 11$ $ BC = 11$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {11} + {11}$ $ AC = 22$